For a face centered cubic lattaice, the unit cell content is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the unit cell content of a face-centered cubic (FCC) lattice, we need to consider the contributions of the atoms located at the corners and the faces of the cubic unit cell.

### Step-by-Step Solution:

1. **Identify the Atoms in the FCC Lattice**:
- In a face-centered cubic lattice, there are atoms located at the corners and in the center of each face of the cube.
- There are 8 corner atoms and 6 face-centered atoms in a unit cell.

2. **Calculate the Contribution from Corner Atoms**:
- Each corner atom is shared among 8 adjacent unit cells. Therefore, the contribution of each corner atom to the unit cell is \( \frac{1}{8} \).
- Since there are 8 corner atoms, the total contribution from corner atoms is:
\[ \text{Contribution from corners} = 8 \times \frac{1}{8} = 1 \text{ atom} \]

3. **Calculate the Contribution from Face-Centered Atoms**:
- Each face-centered atom is shared between 2 adjacent unit cells. Therefore, the contribution of each face-centered atom to the unit cell is \( \frac{1}{2} \).
- Since there are 6 face-centered atoms, the total contribution from face-centered atoms is:
\[ \text{Contribution from faces} = 6 \times \frac{1}{2} = 3 \text{ atoms} \]

4. **Total Unit Cell Content**:
- Now, we add the contributions from the corner and face-centered atoms to find the total number of atoms in the unit cell:
\[ \text{Total unit cell content} = \text{Contribution from corners} + \text{Contribution from faces} = 1 + 3 = 4 \text{ atoms} \]

### Final Answer:
The unit cell content in a face-centered cubic (FCC) lattice is **4 atoms**.

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